A Behavior Tree (BT) [1]}add BT survey is a formalism for plan representation and execution.
Like [2]}, [3]}, we define it as a directed acyclic graph \(G(V,W)\)  with \(|V|\)  nodes and \(|W|\)  edges. It consists of control flow nodes (processors), and execution nodes.
The four basic types of control flow nodes are 1) sequence, 2) selector, 3) parallel and 4) decorator [3]}.
A BT always has one initial node with no parents, defined as Root, and one or more nodes with no children, called leaves.
When executing a BT, the Root node periodically injects a tick signal into the tree. The signal is routed through the branches according to the implementation of the control flow nodes and the return statements of their children. By convention, the signal propagation goes from left to right.
